linearization

[spezialize]

I need to find the linearization for L(x) for f(x)= sqrt(x+1) at x=3.. can anyone give me some steps on how to go about for solving this.

 

[pka]

Well \(\displaystyle L(x) = f(a) + f'(a)(x - a)\) here a=3.

Also \(\displaystyle f(x) = \sqrt {x + 1} ,\quad f'(x) = \frac{1}{{2\sqrt {x + 1} }}\)

 

[spezialize]

so i just plug in 3 into that?

 

[pka]

\(\displaystyle f(3) = \sqrt {3 + 1} = 2\)

\(\displaystyle f'(3) = \frac{1}{{2\sqrt {3 + 1} }} = \frac{1}{4}\)

\(\displaystyle L(x) = 2 + \frac{1}{4}(x - 3)\)